Results 31 to 40 of about 7,081,606 (216)
International Journal of Mathematics and Mathematical Sciences, 1986 In this paper the author obtains new trigonometric identities of the form 2(p−1)(p−2)2∏k=1p−2(1−cos2πkp)p−1−k=pp−2 which are derived as a result of relations in a cyclotomic field ℛ(ρ), where ℛ is the field of rationals and ρ is a root of unity.
Malvina Baica
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Linear Complexity of Generalized Cyclotomic Sequences of Order 4 over Fl
Complexity, 2020 Generalized cyclotomic sequences of period pq have several desirable randomness properties if the two primes p and q are chosen properly. In particular, Ding deduced the exact formulas for the autocorrelation and the linear complexity of these sequences ...
Yuhua Sun +4 more
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The class number of cyclotomic function fields [PDF]
, 1981 Let k be a rational function field over a finite field. Carlitz and Hayes have described a family of extensions of k which are analogous to the collection of cyclotomic extensions {Q(ζm)| m ≥ 2} of the rational field Q.
Rosen, Michael, Galovich, Steven
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Extended Genus Fields of Abelian Extensions of Rational Function Fields
AxiomsIn this paper, we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. For the general case, we use the fact that the extended genus fields
Juan Carlos Hernandez-Bocanegra +1 more
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Mixing Additive and Multiplicative Masking for Probing Secure Polynomial Evaluation Methods
Transactions on Cryptographic Hardware and Embedded Systems, 2018 Masking is a sound countermeasure to protect implementations of block- cipher algorithms against Side Channel Analysis (SCA). Currently, the most efficient masking schemes use Lagrange’s Interpolation Theorem in order to represent any S- box by a ...
Axel Mathieu-Mahias, Michaël Quisquater
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Unification of Chowla’s Problem and Maillet–Demyanenko Determinants
Mathematics, 2023 Chowla’s (inverse) problem (CP) is to mean a proof of linear independence of cotangent-like values from non-vanishing of L(1,χ)=∑n=1∞χ(n)n. On the other hand, we refer to determinant expressions for the (relative) class number of a cyclotomic field as ...
Nianliang Wang +2 more
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Binary Hermitian forms over a cyclotomic field [PDF]
, 2009 Let ζ be a primitive fifth root of unity and let F be the cyclotomic field F=Q(ζ). Let O⊂F be the ring of integers. We compute the Voronoï polyhedron of binary Hermitian forms over F and classify GL2(O)-conjugacy classes of perfect forms.
Yasaki, Dan
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Representation of cyclotomic fields and their subfields [PDF]
Indian Journal of Pure and Applied Mathematics, 2013 Let $\K$ be a finite extension of a characteristic zero field $\F$. We say that the pair of $n\times n$ matrices $(A,B)$ over $\F$ represents $\K$ if $\K \cong \F[A]/< B >$ where $\F[A]$ denotes the smallest subalgebra of $M_n(\F)$ containing $A$ and $< B >$ is an ideal in $\F[A]$ generated by $B$.
Reddy, A. Satyanarayana +2 more
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Wilson's map operations on regulat dessins and cyclotomic fields of definition
, 2009 Dessins d’enfants can be seen as bipartite graphs embedded in compact orientable surfaces. According to Grothendieck and others, a dessin uniquely determines a complex structure on the surface, even an algebraic structure as a projective algebraic curve ...
Streit, M. +3 more
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Blocks of affine and cyclotomic Hecke algebras [PDF]
, 2006 This paper classifies the blocks of the cyclotomic Hecke algebras of type G(r,1,n) over an arbitrary field. Rather than working with the Hecke algebras directly we work instead with the cyclotomic Schur algebras.
Sin ´ead Lyle +3 more
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